This paper reports on an exploration of students' learning derived from the implementation of learning materials developed in a previous collaborative project. The purpose of the study was to examine the development of third-year students' understanding of the Reimann Sum. These concepts were taught to undergraduate teacher trainees wishing to specialize in the teaching of mathematics in the FET (further education and training) school curriculum. The learning materials were developed by mathematics teacher educationists from the University of Witwatersrand, the UKZN (University of KwaZulu-Natal) and the Nelson Mandela Metropolitan University. A group of 31 students participated in the project. The study adopted the APOS (action-process-object-schema) approach within constructivism, as a theoretical framework. Data were generated from students' responses to the collaborative tasks. A genetic decomposition of the Reimann Sum is offered and used as a basis for the analysis. This paper, specifically, reports on the investigation of students' responses based on a learning theory within the context of advanced mathematical thinking and makes a contribution to an understanding of how these students constructed the concepts in a collaborative way. Appended is "The Worksheet with Instructional Tasks." (Contains 5 tables.)